यदि दो रेखाओ के दिक् अनुपात `a_(1), b_(1), c_(1)` तथा `a_(2), b_(2), c_(2)` है तो वे परस्पर लंबवत होगी, यदि -

if quad /_=[[a_(1),b_(1),c_(1)a_(2),b_(2),c_(2)a_(3),b_(3),c_(3)]]

if Delta=det[[a_(1),b_(1),c_(1)a_(2),b_(2),c_(2)a_(3),b_(3),c_(3)]]

Find the coordinates of the centriod of the triangle whose vertices are ( a_(1), b_(1), c_(1)) , (a_(2), b_(2), c_(2)) and (a_(3), b_(3), c_(3)) .

Show that two lines a_(1) x + b_(14) y + c_(1) = 0 and a_(2) x + b_(2) y + c_(2) = 0 , where b_(1) , b_(2) ne 0 are Perpendicular if a_(1) a_(2) + b_(1) b_(2) =0 .

Consider the system of equations a_(1) x + b_(1) y + c_(1) z = 0 a_(2) x + b_(2) y + c_(2) z = 0 a_(3) x + b_(3) y + c_(3) z = 0 If |(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3))| =0 , then the system has

Consider the system of equations a_(1) x + b_(1) y + c_(1) z = 0 a_(2) x + b_(2) y + c_(2) z = 0 a_(3) x + b_(3) y + c_(3) z = 0 If |(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3))| =0 , then the system has

If |(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3))| =5 , then the value of Delta = |(b_(2) c_(3) - b_(3) c_(2),a_(3) c_(2) - a_(2) c_(3),a_(2) b_(3) -a_(3) b_(2)),(b_(3) c_(1) - b_(1) c_(3),a_(1) c_(3) - a_(3) c_(1),a_(3) b_(1) - a_(1) b_(3)),(b_(1) c_(2) - b_(2) c_(1),a_(2) c_(1) - a_(1) c_(2),a_(1) b_(2) - a_(2) b_(1))| is

If |(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3))| =5 , then the value of Delta = |(b_(2) c_(3) - b_(3) c_(2),a_(3) c_(2) - a_(2) c_(3),a_(2) b_(3) -a_(3) b_(2)),(b_(3) c_(1) - b_(1) c_(3),a_(1) c_(3) - a_(3) c_(1),a_(3) b_(1) - a_(1) b_(3)),(b_(1) c_(2) - b_(2) c_(1),a_(2) c_(1) - a_(1) c_(2),a_(1) b_(2) - a_(2) b_(1))| is